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Answer: The answer is (c) One plane can be drawn so that it contains all three points.

Step-by-step explanation:  We are given three points R, S and T in a coordinate plane. Considering all these three points to be distinct and non-collinear, we can draw the following conclusions.

(i) Since each pairs of points. i.e., (R,S), (S,T) and (T,R) give rise to a straight line when joined, so option (a) is incorrect.

(ii) Through any two given points, we can always draw a line. If we consider a third point and since we are dealing with non-collinear points, so one line cannot be drawn through three points.

(iii)We can always draw a line by joining two points and when we join the two ends of the line to a third point which does not lie on the line, it will give rise to a plane. So, option (c) is correct.

(iv) We cannot draw two different planes through three given points. If we do so, the new plane will coincide with the previous one. This proves that option (d) is not correct.

Please see the attached figure, where P, Q and R are three non-collinear points. They give rise to a plane.

Thus, the correct option is (c).

Answer:

y = x divided by three + 7

Step-by-step explanation:

y ≤ 0

Remember that the range is all the possible y-values that the relation can take. We can see in the picture that the repletion is always bellow of the positive y-axis, so the relation can take only negative y-values or zero. In other words, the range of the relation is all the y-values greater or equal than zero, which we represent with the inequality: y ≤ 0. The domain, on the other hand, is all the real numbers; since x can take any value.

Answer:

y ≤ 0 is the correct answer

Step-by-step explanation:

you gots to see it through mah boi

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.

Step-by-step explanation:

Answer:

external pressure

Explanation:

This is the full question:

A sign in front of a store says "No Smoking.” What kind of factor is this sign?

external pressure

internal pressure

media influence

peer pressure

The snowfall during the snowstorm in the White Mountains was 61.5 cm, which is equivalent to 0.615 meters when converted.

To convert the snowfall from centimeters to meters, we need to understand that 1 meter is equivalent to 100 centimeters. With this, to find the snowfall in meters, you simply divide the snowfall in centimeters by 100. So, the snowfall of 61.5 centimeters would be 0.615 meters.

This is because:

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divide total miles by time

725/8 = 90.625 miles per hour

The length of Mr. Webster's exercise room is 18.4 feet, calculated by dividing the area (230 sq ft) by the width (12.5 ft).

To find the length of the room, we can use the formula for the area of a rectangle:

[tex]\[ \text{Area} = \text{Length} \times \text{Width} \][/tex]

Given that the area is 230 square feet and the width is 12 1/2 feet, we can plug these values into the formula:

[tex]\[ 230 = \text{Length} \times 12 \frac{1}{2} \][/tex]

To solve for the length, divide both sides by 12.5:

[tex]\[ \text{Length} = \frac{230}{12 \frac{1}{2}} \]\[ \text{Length} = \frac{230}{\frac{25}{2}} \]\[ \text{Length} = 230 \times \frac{2}{25} \]\[ \text{Length} = 18.4 \][/tex]

So, the length of the room is [tex]\( \boxed{18.4} \)[/tex] feet.

Answer:

Transformation of ΔABC rotation of 180° about the origin .

Step-by-step explanation:

Given : Coordinates of Δ ABC ,=A ( 3,5) , B( 6,1) , C( 0,1) .

Coordinates of Δ A'B'C' = A' ( -3,-5) , B'(- 6,-1) , C'( 0,-1) .

To find :

      Describe the transformation of ΔABC.

Formula used : 180° rotation (clock wise and counter clock wise)

                                   ( x , y ) -------> ( -x , -y ).

Solution :

                   A ( 3,5)-------> A' ( -3,-5).

                   B( 6,1)---------> B'(- 6,-1).

                  C( 0,1).---------> C'( 0,-1) .

Therefore, the transformation of ΔABC rotation of 180° about the origin .

Answer:

Option D.

Step-by-step explanation:

Y-intercept form of the equation of a line is given by y = mx + c

Where m = slope of the line

c = y-intercept

Given equation of a line is x + 4y = 15

We will transform this equation into the y intercept form first.

x + 4y = 15

4y = 15 - x

y = [tex]-\frac{x}{4}+\frac{15}{4}[/tex]

Therefore, y - intercept of this equation will be c = [tex]\frac{15}{4}[/tex]

Option D will be the answer.

Answer: Hello there!

As we know, the dress pants cost a total of $40, and we also know that Skylar has a coupon of y percent in the dress pants and a coupon of z percent in the total purchase.

In this problem, the question is:

Skylar uses the dress pants coupon. Which part of the expression represents the percent that Skylar will pay for the dress pants?

Ok, if we have a discount of y percent, (where y is represented as decimals) means that you are paying the total price of something ( the 100%) minus the the decimal y multiplied by the price of the object.

this is: $40 - y*$40 = (1 - y)*$40

then if the dress pants cost $40, and Skylar only uses the dress pants coupon, he will pay (1 - y)*$40 for the dress pants.

The correct explanation for each expression are;

1. 2x + x + 4 = -17                 Given

2. 3x + 4 = - 17                    Combine like term.

3. 3x = - 21                           Subtraction.

4. x = -7                                Division.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 2x + x + 4 = -17

Now, Solve the expression for x by using suitable property as;

⇒ 2x + x + 4 = -17

Combine like term;

⇒ 3x + 4 = - 17

Subtract 4 both side;

⇒ 3x + 4 - 4 = -17 - 4

⇒ 3x = - 21

Divide by 3;

⇒ x = - 7

Thus, The correct explanation for each expression are;

1. 2x + x + 4 = -17                 Given

2. 3x + 4 = - 17                    Combine like term.

3. 3x = - 21                           Subtraction.

4. x = -7                                Division.

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Answer:

Option a :  [tex]y-300 = 4(x - 100)[/tex]

Step-by-step explanation:

Given :

The drama club sold 100 tickets to a show, it had $300 in profit.

The next show, it had sold a total of 200 tickets and had a total of $700 profit.

To Find :  Equation models the total profit, y, based on the number of tickets sold, x

Solution :

For 100 tickets he had $300 in profit .

⇒ ([tex]x_{1} ,y_{1}[/tex])=(100,300)

For 200 tickets he had $700 in profit .

⇒ ([tex]x_{2} ,y_{2}[/tex])=(200,700)

We will use point slope form i.e.

[tex]y-y_{1} = m(x - x_{1})[/tex] --(A)

Now, to calculate m we will use slope formula :

[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1}  }[/tex]

[tex]m = \frac{700 -300}{200-100}[/tex]

[tex]m =4[/tex]

Now, putting values in (A)

[tex]y-300 = 4(x - 100)[/tex]

Thus Option a is correct i.e. [tex]y-300 = 4(x - 100)[/tex]

The value of another number such that mean remains 13 is 18.

The mean is the average of a data set. Mean gives us the idea of that how much amount of overall data have.

Mean = sum of data / Number of data

For example, if you have marks in 5 subjects like 40,45,44,46,48 then the mean will be

( 40 + 45+ 44 + 46 + 48) /5 = 44.6.

Let's say that number is x

Then,

Mean = (10 + 14 + 8 + 16 + 12 + x)/6

(60 + x)/6 = 13

x = 18

Hence "The value of another number such that mean remains 13 is 18".

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